Question

An arithmetic sequence is shown below. You are not given many terms of this sequence, but you do have enough to fill in the missing number. What number goes in the blank? 14, ,56,....

A.37
B.35
C.21
D.29

Answer 1

B.35

Explanation:

The sequence is

14, ,56,....

14 , x , 56

Think of it as 14 + d = x

x+ d = 56

d is the common difference

We now have 2 equations and 2 unknowns

Substitute the first equation in for x into the second equation

x+d =56

(14+d) +d = 56

Combine like terms

14 + 2d = 56

Subtract 14 from each side

14-14 + 2d = 56-14

2d = 42

Divide by 2

2d/2 =42/2

d = 21

The common difference is 21

Now we can find x

14 + d = x

14+ 21 = x

35 =x

The unknown term is 35